Final Exam
Mechanical Engineering 22.513 with Sherwood at University of Massachuetts, Lowell
About this deck
By: Jen Carr
Created: 2011-05-11
Size: 26 flashcards
Views: 27
Created: 2011-05-11
Size: 26 flashcards
Views: 27
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A finite element model is comprised of what?
Elements, nodes, mesh, material properties
What does each column of the stiffness matrix represent?
The load vector that would need to be applied in order to get a unit displacement at the corresponding degree of freedom
What is an influence coefficient?
Denoted by a12, the static deflection of the system at point 1 due to a unit force applied at point 2 when the unit force at point 2 is the only force acting
What is Maxwell's reciprocal theorem?
a21=a12, since path of load application should not affect resultant potential energy total of an elastic system
With respect to derivation of element, what dictates order of polynomial for displacement field?
Number of degrees of freedom
What is a functional?
An integral expression that implicitly contains differential equations that describe the problem
What is the B matrix?
Relates nodal displacements to strain field
What is a consistent load vector?
Derived using shape function that is consistent with the element formulation
How do you recognize the shape function matrix?
Relates nodal displacement (d) to displacement field; it is whatever products/ terms that relate the nodal displacement vector to the assumed displacement field
How is tensorial shear strain related to engineering shear strain?
epsilon xy = 1/2 gamma xy
How do you show that the 3-noded triangular element with 6-DOF is a constant strain triangle?
epsilon x, epsilon y, gamma xy are constant because du/dx and dv/dy are constants
In the Raleigh-Ritz method, what are your DOFs?
Generalized coordinates, aka coefficients (a0, a1, a2, etc)
Where are the stress values within an element most accurate?
At the Gauss points
How can you tell between the strong and weak form of the governing partial differential equation?
In the strong form the derivatives are continuous for all orders. The weak form has relaxed continuity requirements
Why use Gauss quadrature for isoparametric elements?
Can't do quad elements algebraically, must be done numerically
What lesson was learned fom the plasma cutting torch electrode?
You must change the boundary condition of the temperature of the tungsten at the electrode when finding how well the water bath cools the system. A flux condition should be chosen
How do you know a finite element solution has converged?
Plot the mesh density vs. solution and see asymptote
When deriving an element, what conditions need to be satisfied?
The equation needs to be complete and admissible (satisfy essential boundary conditions)
How many DOFs are in a brick element?
3 (translation only)
Give an example of when to use skew supports.
Using non-perpendicular supports on a truss or a tank in a trussel
When do you use implicit vs. explicit FE code?
Implicit is used for static to quasistatic situations (few time steps). Explicit is used in high speed impact analysis (many elements and time steps).
How and why would you use explicit code in quasistatic situations?
you need to do mass or time scaling. You would do this because contact algorithms are better in explicit codes
What does rank deficient mean?
That the rank of [K] is less than the number of element DOFs - number of rigid body modes. The rank of a matrix is the maximum number of independent rows or columns.
About this deck
By: Jen Carr
Created: 2011-05-11
Size: 26 flashcards
Views: 27
Created: 2011-05-11
Size: 26 flashcards
Views: 27
About StudyBlue
STUDYBLUE makes things that make you better at school.
Things like online flashcards with photos and audio.
Things like personalized quizzes and friendly reminders about when (and what) to study next.
Think of it as a digital backpack™: access to all of your study materials online and on your phone.
STUDYBLUE exists to make studying efficient and effective for every student, for free. Join us.
“Simply amazing. The flash cards are smooth, there are many different types of studying tools, and there is a great search engine. I praise you on the awesomeness.”
Dennis
Dennis